answer may vary depending on size of square
5 equilateral triangles.
hexagon
Well, isn't that a lovely question! In a 4x4 grid, you have 30 squares in total. You see, there are 16 1x1 squares, 9 2x2 squares, 4 3x3 squares, and 1 big 4x4 square. Isn't it just delightful to see all those squares come together to create something beautiful?
50
Assuming each of the smallest squares (i.e., each of the 16 ones forming the large square) has a side 1 unit long: There are 16 squares that are 1x1. There are 9 squares that are 2x2. There are 4 squares that are 3x3. And there is 1 square that is 4x4. So the total number of squares is 30.
72cm
A "six sided shape" is a hexagon. The solid formed by 6 squares is a cube (four sides, top, bottom).
The answer is hexagon because if it is formed by curved, line segments, or both it is definitely hexagon!
In a square with 25 smaller squares arranged in a 5x5 grid, there are a total of 55 squares. This includes the 25 individual smaller squares, the 16 squares formed by combining 4 smaller squares, the 9 squares formed by combining 9 smaller squares, the 4 squares formed by combining 16 smaller squares, and the 1 square formed by combining all 25 smaller squares.
A large compound formed by the joining of smaller compounds is called a polymer.
Diagonals in an hexagon: 0.5*(6^2 -3*6) = 9 diagonals
hexagon
The three major diagonals in an ordinary hexagon do not intersect at the same point. Therefore, in such a hexagon, the diagonals form 111 triangles.
5 equilateral triangles.
Equilateral triangles have three 60' angles, and the angles of any triangle always add to 180'. Attaching squares to each side of an equilateral triangle would also form three obtuse angles (360' - 90'- 90' - 60' = 120') and the resultant obtuse Isosceles triangles' hypotenuses would be greater in length than any side of the square since its two equal sides are the same length as the square. However, the angles of any corner of the newly formed hexagon would be 90' from the square plus 30' (30' = (180' - 120')/2) from the obtuse triangle, making this hexagon equiangular, but not equilateral. JCS
Draw incircle and circumcircle. radius of incircle = 6 radius of circumcircle = 6 × 2/√3 = 12/√3 (side opposite to 60° is √3/2 times hypotenuse. consider right angled triangle formed by these two radius and 1/2 side of hexagon. (1/2 side)² = (12/√3)² - 6² = 12 1/2 side = √12 full side of hexagon = 2√12, perimeter = 12√12 Area = 1/2 a × perimeter = 1/2 × 6 × 12√12 = 36√12 = 72√3 unit²
hexagon